On your computer graphics journey, you will eventually run into some paper or code mentioning spherical harmonic functions. They are indeed a very useful tool: with just a few coefficients, they allow us to approximate a given function defined on a sphere. This can be very useful for modeling complex lighting.
Picture this, the year is 1996. You find yourself frustrated with the incumbent search engines like AltaVista, which primarily does a content-based search (it'll give you an article on "Hotels for Chickens" if you search "Hotels" because the word matches). There's gotta be a better way, right? Well, in hindsight, of…
Does a new algorithm that improves on Dijkstra'a classic one actually deliver a practical benefit for networking?
If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your…
a personal blog
A more explicit example
How does the geometry of a road unfold?
Benchmarks & Tips for Big Data, Hadoop, AWS, Google Cloud, PostgreSQL, Spark, Python & More...
When Mathematica seems to not to know how to simplify an expression, it may be doing the right thing, being more sophisticated than you expect.
Tauformer is a topological transformer (see paper ) that replaces dot‑product attention with a Laplacian-derived scalar (taumode) per token/head, then attends using distances in that scalar space. Below is a post-style overview of the idea and the first training signals from a 30M-parameter run.
An aggregation is some kind of summary of a set of data. This can be the sum, length, minimum, etc. It is quite common to want to calculate such a summary repeatedly, e.g. “the maximum noise level in dB for the past 30 seconds” for a nuisance detector. In such a case we say there is a sliding window over our data, and…
A hands-on introduction to elliptic curve cryptography. Start with curve geometry, build point addition and scalar multiplication, see why ECDLP is hard, and then use that math in ECDH, ECDSA, and ECIES.
In 2005 Google showed off Google Maps, which lets you drag the map around instead of reloading the page like MapQuest and others used. That’s the feature that got everyone’s attention. But what got my attention was a feature they added in 2007 where you could drag the start/end points on a route [1] , and it would…
I’m sure that some pictures are worth a thousand words, but others trigger a whole lot of puzzlement. Such was the case with the cover of a book I recently bought entitled Calculating with Tones: The Logarithmic Logic of Music:
In 1980, Intel released the Intel 8087 floating-point coprocessor, a chip that could make math up to 100 times faster. As well as arithmetic...
Many people in the U.S. believe that their statistical knowledge is limited, but they would rely on statistics for decision-making more if they understood statistics better, according to a new study led by a Penn State researcher.
Made in Notion, the connected workspace where AI agents and teams organize docs, projects and knowledge together.
Every once in a while the internet gets talking about Geometric Algebra (henceforth GA) and how it’s a new theory of math that fixes everything that’s wrong with linear algebra and multivariable calculus. When I come across this stance I am compelled to respond with something like: “wait wait, it’s not true! GA is…
The Jazz of Physics: Albert Einstein and John Coltrane had a lot in common. The so-called “Coltrane circle” or “Circle of Fifths,” but incorporates Coltrane’s own innovations. Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in the Repository of Scales and
New research indicates that AI agents learn compressible models of data, which don’t have enough space to enable memorization.
Calculus is the mathematics of approximations of continuous quantities ; number theory asks exact problems about discrete quantities. These seem, therefore, to be unrelated studies.
Fully discrete methods dominated for a few years, but language models based on continuous diffusion are making a comeback.
Bennett, an American physicist at IBM Research, and Brassard, a Canadian computer scientist at the Université de Montréal, are widely recognized as founders of quantum information science, a field at the intersection of physics and computer science that treats quantum mechanical phenomena not merely as properties of…
Math as cultural institution.
Practice machine learning engineering with hands-on coding challenges. Implement neural network components, backprop, and more — from scratch.
One of the oldest theorems in mathematics is that there are infinitely many primes. Euclid (the geometer!) proved this around 300 BCE, and for centuries afterwards the story ended there. There are infinitely many primes -- so what else is there to ask about them?
Reddit user xilefakamot created this in 2020 — a “topologist’s map of the world.” It depicts international borders and nothing else — the shapes, sizes, and distances between countries are forsaken in order to present the pattern of their borders as efficiently as possible. “No calculations per se – I sketched out a…
A visual and intuitive intro to complex number system providing a historical overview of how it was developed and why it is useful.
How Devin and a Cognition researcher built the world’s highest-performance GPU lattice siever, to make factoring numbers 10x cheaper than the previous…
